help-33

[sacred idol]

.close

[marsh citrus]

Channel closed

Closed by @sacred idol

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ornate socket]

can someone help me? i have been stuck on this question for a while

[rancid geode]

which question in particular?

[ornate socket]

both

[rancid geode]

right

[ornate socket]

for part A, I am getting -4, -6, and part be -5, -11

[rancid geode]

do u understand how reflection works

[ornate socket]

yh

[rancid geode]

cool

[ornate socket]

but

the platform keeps telling me its wrong

[rancid geode]

the second one seems odd

[ornate socket]

yh

i mixed it up

with another question

mbmb

[rancid geode]

still odd?

[ornate socket]

it is?

idk what i did wrong

[rancid geode]

what does it mean to translate it by ${\binom{-1}{-5}}$?

[ornate socket]

is it not just -4-1,-6-5?

[elfin berry]

k

[rancid geode]

the x-axis is correct

[ornate socket]

to move left by 1 and down by 5?

[rancid geode]

wait

a

sec

i misread the question

mb

oh ye

[ornate socket]

yh?

[rancid geode]

looks abt right

perhaps, (-4, -6) and (-5, -11)

[ornate socket]

alr, lemme check with the platform rq

[rancid geode]

with the brackets?

[ornate socket]

still wrong...

idk how its wrong

[rancid geode]

oh fuck

i got it

its x = -1

not y = -1

i should lay down 😭

its a reflection across a line parralel to the y-axis

not x-axis

[ornate socket]

but it says reflected in x=-1?

no?

[rancid geode]

u did

y = -1

[ornate socket]

huh?

[rancid geode]

x = -1 is a vertical line

[ornate socket]

ohhh

icic

[ornate socket]

right

thx

.close

[marsh citrus]

Channel closed

Closed by @ornate socket

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drowsy topaz]

guys help Idk if I did the right thing

[hexed junco]

Cant really see if you did the right thing if we dont know what you did

[novel juniper]

are you allowed external help on this

[stoic saddle]

You have attempted this problem 0 times.

[marsh citrus]

@drowsy topaz Has your question been resolved?

[drowsy topaz]

Mbd I sent the wrong picture

[vital oracle]

this one also says "You have attempted this problem 0 times." on it, you can click submit answers and see how much of it is correct
we would have 6 other attempts to get it right

however for (B) I will say youre misunderstanding the question

"horizontal" does not just mean 0 is automatically the answer

[drowsy topaz]

nvm I just saw that I have to write none instead of 0

Ik😭😭

[tired knoll]

Can you show your work?

[vital oracle]

yep then its correct

[drowsy topaz]

ok yes I got the right answer thanks guys

.close

[marsh citrus]

Channel closed

Closed by @drowsy topaz

Use .reopen if this was a mistake.

[vital oracle]

np

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tiny elk]

what is the limit definition of a sequence?

[tired knoll]

What does Google have to say about it?

[tiny elk]

I ask this not because I have not googled it but because textbooks (and google) kind of say the same thing but the definition is never exactly the same, for example

• for each M in R there exists n_M in N such that a_n > M for each n > n_M
  or
• for each M>0 in R there exists n_M in N such that a_n > M for each n > n_M
  or
• for each M in R there exists n_M in N such that a_n > M for each n >= n_M

(for limit n->+inf (a_n) = +inf)

[vagrant raft]

they are all equivalent

[wary kite]

i mean these say the same thing

[tiny elk]

but then, why choose to say M>0

[vagrant raft]

why not

if you don't want to you don't have to

[wary kite]

because it captures the idea of saying the limit is positive infinity more

it isn't that big of a deal

[tiny elk]

what about this one?

what if a_n is exactly -M

[wary kite]

what is this delta_n

oh a

[wary kite]

it wouldn't matter since it holds for all M

the information added by using <= instead of < is essentially nothing

[tiny elk]

yeah it's kind of hard to understand how adding information changes nothing

[wary kite]

because M is arbitrary we know the statement holds for larger M as well, making the equality case for any particular M meaningless

lets do the +inf definition instead to use positive numbers

if we can guarantee that for any M > 0there exists n_m so that for all n > n_m,
a_n >= M then we also know there is an index after which all of the sequence members are larger than M + 1 since M + 1 > 0 and we know we can find n_m for any positive number

but this makes the equality for M pointless

do you understand what i mean?

[tiny elk]

yeah I get it

thanks

[wary kite]

no worries

[tiny elk]

one more thing

a sequence is not limited iff for each M in R there exists n_M in N such that a_(n_M) > M

[wary kite]

yea

are you asking how this is different?

from the limit

[tiny elk]

what about for each M in R there exists n_M in N such that a_(n_M) < M

[wary kite]

this would be unbounded below

i think they just meant unbounded above

[tiny elk]

can I use here M>0 or M<0?

like does it change anything

[wary kite]

uhh it depends on what you're trying to prove

[wary kite]

it can

for example, if $a_n = \frac{1}{n}$

[elfin berry]

knief

[tiny elk]

I get it

[wary kite]

if we used M < 0 in your definition then this would automatically be satisfied

but clearly this isn't unbounded

[wary kite]

since all of the terms are greater than any negative

[tiny elk]

so for unbounded definition it's better to just say M in R

[wary kite]

if you want to say unbounded above then use M > 0 and if you want to say unbounded below say M < 0

and a_n > M and a_n < M respectively

[tiny elk]

alright

thanks again

[wary kite]

you're welcome

[tiny elk]

.close

[marsh citrus]

Channel closed

Closed by @tiny elk

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unborn burrow]

my professor taught me I’d its washer or disk, I derive with the opposite of the axis of rotation

So it ahould by with respect to dx

Why is it dy

And if its shell, then its the same

He said Disk/washer, integrate in terms opposite the axis. So if you're rotating around y = something, it's dx. If you're rotating around x = something, it's dy.
Shell - integrate in terms of this axis. If you're rotating around y = something, it's dy. If you're rotating around x = something, it's dx.

[amber birch]

the heights are the distances from the y-axis

and the distances from the y-axis are horizontal lengths

so the width of the rectangles are vertical lengths = you should use dy

also your prof isn't wrong: you're rotating around x = 0 after all

x = something is a vertical line

[unborn burrow]

I’m kinda confused cuz I took it as a general rule to always apply

Is this a special case since the y and x are both 0 to 1?

Lets assume that

The rectangle isn’t there

Cuz most test questions it isn’t

I wanna understand for future questions

When to use dx and dy

[marsh citrus]

@unborn burrow Has your question been resolved?

[unborn burrow]

No

[marsh citrus]

@unborn burrow Has your question been resolved?

[marsh citrus]

@unborn burrow Has your question been resolved?

[marsh citrus]

@unborn burrow Has your question been resolved?

[marsh citrus]

@unborn burrow Has your question been resolved?

[bitter badger]

The reason the problem uses dy is because the Disk/Washer Method requires the slice to be perpendicular to the axis of rotation. Since you are rotating around the vertical y-axis (the line x=0), the representative disk must be created by a horizontal rectangle, and a horizontal rectangle's thickness is dy. Your professor's shortcut, "If rotating around x=something, integrate dy," is correct because the y-axis is the line x=0. Consequently, because the integration is ∫πR²dy, the radius R must be a function of y, forcing the required algebraic conversion of the function from y=x^(2/3) to x=y^(3/2)

[past trellis]

these might help
Ring
Cylinder
Other stuff

[bitter badger]

In general, the variable of integration depends on the orientation of the slices relative to the axis of rotation. For the Disk/Washer Method, slices are perpendicular to the axis of rotation, so you integrate with respect to the variable that moves perpendicular to that axis. This often means using dx when rotating around a horizontal line (like the x-axis) and dy when rotating around a vertical line (like the y-axis). For the Shell Method, slices are parallel to the axis of rotation, so you integrate with respect to the variable that moves along the same direction as the axis (dy for a horizontal axis and dx for a vertical one). In short: disks/washer → perpendicular variable; shells → parallel variable.

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[still temple]

<@&268886789983436800>

[fallow mesa]

Miku

[sick charm]

The three vertices can be on three sides, or on two side.

[still temple]

what have u tried?

[fallow mesa]

Um

I tried thinking

And failed

T-T

[still temple]

so there is a technique in enumerative combinatorics called complementary counting

i believe it may be useful here

have you heard about it?

[fallow mesa]

How does it work?

Dont think so

[still temple]

if you have heard of probability, then it basically says that the probability of an event A happening + the probability of the complementary event happening (not A) = 1

this is actually directly related to combinatorial problems

[fallow mesa]

Wait is it nCr?

[still temple]

yes

almost

you will need that formula

[fallow mesa]

I know the formula but idk how to use it here

[still temple]

imagine a plane in front of you

a grid

if I give you 3 points and tell you to connect a line between each pair

are they guaranteed to be a triangle?

[fallow mesa]

Yes?

[still temple]

what if their y or x coordinate is the same?

[fallow mesa]

If they are in the same line then no?

[still temple]

for all three

exactly

so we can use complementary counting to find all the possible ways of choosing such points and then subtract the cases we don't want

this will give us the cases we do want

[fallow mesa]

Oh

[still temple]

we can't have all three points chosen from one side of that square, basically

because then we wouldn't create a triangle

we would create a line segment

[fallow mesa]

So I subtract every outcome of them being on the same line

[still temple]

yes!

[fallow mesa]

16C3-3C3-5C3-4C3-4C3?

[still temple]

bingo

nicely done

[fallow mesa]

Oh thank you

[still temple]

happy to help

[marsh citrus]

@fallow mesa Has your question been resolved?

Channel closed

Closed by @fallow mesa

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[knotty trellis]

Prove that MI bisects AD

[knotty trellis]

I is the incenter, M is midpoint of BC

D is where the incircle touches BC

i have no idea how to start here

AD and MI

i have to prove that MI bisects AD

[blazing dew]

can you send the original question?

[knotty trellis]

what does that mean?

[knotty trellis]

Given a triangle ABC with an incircle centered at I, touching BC at D and a midpoint of side BC M, prove that MI bisects AD

[blazing dew]

any triangle?

[knotty trellis]

yes

yes, just like on the pic

otherwise it wouldnt necessarily intersect AD

[blazing dew]

can you just prove it by contradiction?

[knotty trellis]

how would u do that?

[blazing dew]

just an idea

assume they are parallel and lead to a contradiction

[knotty trellis]

okay so prove that AE = DE

[knotty trellis]

its not just that they intersect

bisects means that AE = ED

or that MI goes through midpoint of AD

[blazing dew]

oh wait i forgott

somehow switched bisect v intersect

[knotty trellis]

oh

https://math.stackexchange.com/questions/1850069/prove-on-incenter-and-mid-point

just managed to find this on stack exchange

it uses barycentric coords

pretty interesting

I'll close this now ig, thx

.close

[marsh citrus]

Channel closed

Closed by @knotty trellis

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drifting briar]

@marsh citrus

[drifting briar]

hi @marsh citrus

<@&286206848099549185>

[calm harbor]

Do you have a question?

[drifting briar]

yes

[calm harbor]

Alright, can you post it?

[drifting briar]

logitude latitude

/ok wait

look i posted it

<@&286206848099549185> help me with this question

[blazing dew]

zoom better

[drifting briar]

@calm harbor dude are you there?

ok

im posting @blazing dew

done

you got anwer?

[blazing dew]

can you put it on the table and then take a pic?

[drifting briar]

bruh ok fine

[calm harbor]

It’s very blurry

[blazing dew]

and it looks more like a reading exercise than a math exercise

[drifting briar]

it is longitude and latitude

longitude latitude understand?

[blazing dew]

that's better to read

[drifting briar]

ok

got answer?

anyone there?

[blazing dew]

do you only want the answer?

!nosols

[marsh citrus]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[drifting briar]

yes

ony answer

pls

[blazing dew]

the simple ans: Eastern states like Assam experience sunrise earlier than western states like Gujarat because they are located farther east. Since the Earth rotates from west to east, the eastern parts of a country see the sun rise and set earlier than the western parts.

[drifting briar]

ok tysmm

[blazing dew]

close the channel @drifting briar

[marsh citrus]

@drifting briar Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[blazing dew]

"The sum of n real numbers is zero and the sum of their pairwise products is also
zero. Prove that the sum of the cubes of the numbers is zero."

[blazing dew]

I've just started exploring the "Mathematical Olympiad Challenges" book but I've some problems figuring out where to start when encountering problems.

<@&286206848099549185>

anyon here to help?

<@&286206848099549185>

[marsh citrus]

@blazing dew Has your question been resolved?

[fickle fractal]

hi

[blazing dew]

hi

[weak surge]

Interesting question i will think about it

[blazing dew]

wait i have an idea

so we have $n_1 + n_2 + ... = 0, n_1 n_2 + n_2 n_3 + ... = 0$, which means we have $n_1^2 + n_2^2 +... = 0$ also

[elfin berry]

Thomas

[weak surge]

[blazing dew]

and we know that $n_1^2 \ge 0$ so that means that $n_1, n_2, ... = 0$

[elfin berry]

Thomas

[blazing dew]

which should be done

[weak surge]

very nice

[blazing dew]

well time to move on to the next one

do I add all of the terms together?

[weak surge]

hmm

not necessarily

because there are ways that a + b + c + d - a^2 - b^2 - c^2 - d^2 ≥ 1

Can you make use of the cyclic nature in any way?

[blazing dew]

lemme see

we have $x^2 \ge x - \frac{1}{4}$ right?

[elfin berry]

Thomas

[blazing dew]

we have $a > b^2 + \frac{1}{4} \ge b$

[elfin berry]

Thomas

[blazing dew]

if we do this to every equation, we have a contradiction

Looks symmetric

<@&286206848099549185>

[past trellis]

i would let x=y=z

there might be more solutions

[past trellis]

so $2x=\sqrt{4x-1}$

[elfin berry]

Allen

[harsh scroll]

do you still need help?

[marsh citrus]

@blazing dew Has your question been resolved?

[blazing dew]

yeah

was gone for a while

guess no one's here

.close

[marsh citrus]

Channel closed

Closed by @blazing dew

Use .reopen if this was a mistake.

[ornate shale]

Ehh

There're

[blazing dew]

.reopen

[marsh citrus]

✅ Original question: #help-33 message

[elfin berry]

Poly(^///^)

[ornate shale]

I'm just too lazy to explain

[blazing dew]

how'd you do that??

[ornate shale]

Oh I made a mistake here

[ornate shale]

Do what

The LaTeX?

[blazing dew]

spawn in the whole thing

[ornate shale]

I Latex this 40min ago while you were gone

[elfin berry]

Poly(^///^)

[blazing dew]

and how'd you make it spawn again without repeating the cmd?

[ornate shale]

I just deleted the command so it won't be a wall text

[blazing dew]

oh nice to know

btw, do you have some tips for olympiad math?

[ornate shale]

Noo... I've never done Olympiad better ask someone else

Oh wait I do know a place

https://discord.gg/3sbwZdh

[blazing dew]

welp i'm done for today

.close

[marsh citrus]

Channel closed

Closed by @blazing dew

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[acoustic storm]

hi im trying to find the shortest distance between a point and a line. is the statement ive written correct?

[acoustic storm]

I had solved the question using the dot product of OX and XA, but the markingscheme uses OX dot AX. They'd be the same right

[jagged relic]

They're both 0, so yes

[acoustic storm]

awesome. it wouldnt matter even if the angles arent perpendicular right

[jagged relic]

It would

They have opposite sign

[acoustic storm]

how so? i tried drawing it out and using the equation |v||w|cos(theta) to try to understand, but i didnt get it

[jagged relic]

You're probably not taking the cos of the correct angle

If you extend AX in your drawing, the LHS uses the angle on the right of X while the RHS uses the angle above X

They add up to 180°, meaning their cos are opposites

[marsh citrus]

@acoustic storm Has your question been resolved?

Channel closed

Closed by @acoustic storm

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pulsar plume]

Let's say I have found out the solution for a differential equation.

In this case, that's the correct solution but in the future if I solve a diff equation and need to quickly check if my solution is correct, how can I do it using desmos(or other graphing calculators)?

How can I visually verify the solution in the picture is correct or not using desmos?

[blazing dew]

,rccw

[marsh citrus]

@pulsar plume Has your question been resolved?

[pulsar plume]

I have asked this before and didn't get an answer, is it not possible?

[jagged relic]

I don't understand what your solution corresponds to. Can you post the original question?

[pulsar plume]

@jagged relic

That's a solution to the DE above it.

The question doesn't matter, how can I quickly verify my solution to a DE?

Like I can verify my solution to an indefinite integral by differentiating the solution and see if it matches with the original integrand.

[jagged relic]

That's a solution to the DE above it.
I don't see how, which means either I'm missing context or you made a mistake. That's why I'm asking for the original.

[pulsar plume]

Maybe I have made a mistake, lemme try from the start and send the entire solution here

[pulsar plume]

I believe this is correct. Maybe a calculation mistake on my solution before

How to verify if this solution is correct using a graphing calculator?

[marsh citrus]

@pulsar plume Has your question been resolved?

Channel closed

Closed by @pulsar plume

Use .reopen if this was a mistake.

[marsh citrus]

@pulsar plume Has your question been resolved?

[marsh citrus]

Channel closed

Closed by @pulsar plume

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mossy widget]

i need help plz

idk how to tackle this

this is all ive written so far

so is omega a tangent vector for an arbitrary path at the identity matrix?

anyone???

i need some hints

[marsh citrus]

@mossy widget Has your question been resolved?

Channel closed

Closed by @mossy widget

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[marsh citrus]

Please don't occupy multiple help channels.

[elfin badger]

can someone help me with part c

[fervent rampart]

what they did was
\begin{gather}
Ax = b \
\implies A\inv A x = A\inv b \
\implies x = A\inv b
\end{gather}

[elfin berry]

κλαουντ ☁ (cloud)

[elfin badger]

im not sure why they've put this here

[fervent rampart]

so step 1 -> step 2 was multiplying both sides on the left by A^(-1)

[elfin badger]

wouldnt it be 1/3

[fervent rampart]

and they get 1/3 as the first entry of x, in the last line don't they?

[elfin badger]

this is the question but the figures are differennt

[pearl haven]

do you know what's cramer's rule

[elfin badger]

yh

[pearl haven]

so what will be the value of z here

[pearl haven]

yes, so notice that youre using 2 determinants here

one is of matrix A as it says in the question

the second one is delta Z

do you know how do we obtain delta Z?

[marsh citrus]

@elfin badger Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sweet sparrow]

Prove these inequalities are true:

[sweet sparrow]

(note: I have solved this before using trig identities but now the book wants us to do this using properties of increasing/decreasing functions)

[stoic saddle]

3 arctan(x) - 4 arctan(x+1) + arctan(x+2) ?< 0

uhhhh jeez

see my first thought is fucking jensen or other concavity shit

but that looks like its not the route your book wants

[sweet sparrow]

namely:

• if f'(x) >= 0 in (a; b) and there exists at least one point x so that f'(x) > 0 -> f(b) > f(a)
• if f(a) < g(a) and f'(x) < g'(x), x is in (a;b) -> f(x) < g(x), x in [a;b]

[sweet sparrow]

guess what, this problem appears yet again a few lines later in concave/convex functions part

this book is dumb ik

[stoic saddle]

aight hold up

let me just abbreviate arctan(x) as a(x)

$3a(x) + a(x+2) \overset?< 4 a(x+1) \iff 3a(x) - 3a(x+1) \overset?< a(x+1)-a(x+2) \iff 3(a(x+1)-a(x)) \overset?> a(x+2)-a(x+1)$

[elfin berry]

Ann

[stoic saddle]

are we allowed to use the known derivative of arctan(x) at least

[sweet sparrow]

yes

[stoic saddle]

aight

are we allowed lagrange MVT

[sweet sparrow]

yes

[stoic saddle]

then this becomes $3a'(c_1) \overset?> a'(c_2)$ where $0<x<c_1<x+1<c_2<x+2$

[elfin berry]

Ann

[sweet sparrow]

oh i got it now, thanks

.close

[marsh citrus]

Channel closed

Closed by @sweet sparrow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[untold plinth]

My question is on [Algebraic Topology : Delta Complexes]

[untold plinth]

Hi, I've drawn these complexes on $S^2$ and just want to verify that the two on the left are not Delta-complexes on $S^2$ as they violate the second rule in the definition given in Hatcher: "(ii) For a face $F_i^n$ of $\Delta_n$, the restriction $\sigma_\alpha |{F_i^n}$ must already be a path $\sigma\beta$ on the $(n-1)$ standard simplex". It might be a trivial observation but here the 3 faces of $\Delta_2$ are mapped onto a single 1-simplex, which feels like (to me) violating this rule.

[elfin berry]

Emir Yusuf

[marsh citrus]

@untold plinth Has your question been resolved?

[untold plinth]

As much as I think, it feels like a violation but I can't put my hand on the exact step of violation. To not violate the first rule "(i) Restricting a simplex to an interior has to result in an injective map" I believe we have to glue three faces of a triangle consecutively along edge a, e.g. in the leftmost complex, but then, the restriction to a face does not result in an already existing map on an (n-1) simplex, therefore violating the second rule.

[marsh citrus]

@untold plinth Has your question been resolved?

[untold plinth]

In this hour I have resolved the question myself, my intuition was correct.

.close

[marsh citrus]

Channel closed

Closed by @untold plinth

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[atomic lagoon]

<@&268886789983436800>

[atomic lagoon]

.close

[marsh citrus]

Channel closed

Closed by @atomic lagoon

Use .reopen if this was a mistake.

[pallid jolt]

.reopen

[marsh citrus]

✅ Original question: #help-33 message

[pallid jolt]

What

[pallid jolt]

Hey heads up in future you’re more likely to get a reply in #alg-top-geo-top

[pallid jolt]

Okay please don’t randomly ping mods in future. It makes it harder for us to respond to real mod pings. Thanks

.close

[marsh citrus]

Channel closed

Closed by @pallid jolt

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[clear hill]

I need help with these 2

[tribal roost]

For the first problem you can count the number of possibilities including a certain point

and do that for every point

[clear hill]

i dont get it

so i just count all the possibilities

[tribal roost]

take one point

let's say one in the corner

[clear hill]

ok

[tribal roost]

How many possibilities with this point ?

[clear hill]

3

[tribal roost]

yes

[clear hill]

so i just do that for every point?

[tribal roost]

then take one in the center

no

[clear hill]

6

[tribal roost]

there is only 3 types of points

[clear hill]

ohhh

[tribal roost]

not 3 ?

[clear hill]

uhhh

4

its 4 i htnk

think

[tribal roost]

like th 3 directions in space

[clear hill]

o

wait

[tribal roost]

there is just one in the center btw

[clear hill]

you can go up across

and diagonal twice?

[tribal roost]

ohhhh

I forgot abt that yes

soo

[clear hill]

ok

[tribal roost]

7

no ?

4 diags

[clear hill]

whut

[tribal roost]

3 directions

[clear hill]

?

[tribal roost]

oh no

2 diags

[clear hill]

yeah

[tribal roost]

ye alr so 5 total ?

[clear hill]

wh

what

[tribal roost]

because 1 up

[clear hill]

yes

one across

and 2 diagonal no?

[tribal roost]

ye

[clear hill]

thats 4

[tribal roost]

and one coming to us

if it's in front of us

[clear hill]

wait

what

[tribal roost]

it's 3x3

[clear hill]

\yes

[tribal roost]

so there's 3 directions

[clear hill]

yes

[tribal roost]

from the center

[clear hill]

up down and diagonal?

[tribal roost]

like x y and z

[clear hill]

yeah

yeah

[tribal roost]

plus the two diags

alr so 5 for the center one

[clear hill]

huh?

[tribal roost]

3 for the corners

[tribal roost]

no ?

[clear hill]

there is only 4?

the two diagonals and up and across

[tribal roost]

there is up , across and since it's in 3d then there is a third one

[clear hill]

?

[tribal roost]

look up this

oh

bruh

sry Im so dumb

when I said 3x3 I though 3x3x3

[clear hill]

o

[tribal roost]

it's not at all

[clear hill]

ok

[tribal roost]

oh well it's much simler now lol

[clear hill]

also you can make lines using the other squares

like AHI

[tribal roost]

wdym ?

[clear hill]

look at the attatched problem

it says so in the question

that lines like that count

[tribal roost]

oh ok

so it is 3d but the game is slightly different

[clear hill]

uhhh

i guess so

[tribal roost]

it's kinda if you had 3 parallel universes interacting

with the three games

[clear hill]

huh

oh

yeah

[tribal roost]

ok no I was right in the first place

for the middle one there is 7 possibilities

[clear hill]

huh

wait brb

[tribal roost]

just think of it in 3D

k

to visualize better I make a square box with my hands in front of me

idk if it can help

[clear hill]

ok im back

@tribal roost

[tribal roost]

I made a scheme

1 sec

[clear hill]

ok

[clear hill]

yes

[tribal roost]

I only put A

but you can imagine the rest

also sry it's flipped

well anyway

[clear hill]

ok

its fine

[tribal roost]

if on the first like plane

you take the center

so it should be E

[clear hill]

yes

[tribal roost]

let's say they are arranged from closer to us to further and from left to right top to bottom

so E

[clear hill]

?

[tribal roost]

how many possibilities ?

[tribal roost]

well on the first surface you have

A B C
D E F
H I J

[clear hill]

yes

[tribal roost]

that's on the one closer to us

[clear hill]

yes

[tribal roost]

then there is K L M
etc

[clear hill]

ABC
DEF
GHI

yes

[tribal roost]

😅

anyway

what

no

oh bruh

[clear hill]

?

[tribal roost]

idk my alphabet that's terrible

bcs I was trying to recite it in english

anyway

[clear hill]

o

ok

[tribal roost]

how many possibilities for E ?

count the ones one the face itself first

[clear hill]

4

[tribal roost]

on the face ye

[clear hill]

yes

[tribal roost]

but then there is one more

as you said

[clear hill]

arent there many more

for e

[tribal roost]

I don't think so

[clear hill]

yeah

[tribal roost]

If the number of points around was infinite

there would be as much as for the center point of the cube

but it's limited

so only 5 for E

[clear hill]

wheres the 5th one

[tribal roost]

It's through the cube

Ill just write it down t be more clear

[clear hill]

ABC JKL
DEF MNO
GHI PQR

so

BEH

DEF

AEI

CEG

MEO

JER

it works like that

so there are much more possibilities?

[tribal roost]

A B C
D E F
G H I

J K L
MNO
P Q R

S T U
V W X
Y Z µ

[clear hill]

yes

[tribal roost]

oh ok

[clear hill]

so there are many

more

[tribal roost]

well I see the problem

[clear hill]

for E

yes?

[tribal roost]

we didn't understand it the same way

[clear hill]

wdym

[tribal roost]

I thought of it like in 3d if it's real tic tac toe

[clear hill]

yes

[tribal roost]

but in 3d

and it maes sense with the exemples they gave

[clear hill]

yes

waot

[tribal roost]

but your interpretation also makes kinda sense

[clear hill]

wait

[tribal roost]

although I think mine is what they rly meant

[clear hill]

so how did you interpret it?

[tribal roost]

If it was like you said it would be less like tic tac toe in 3d

just like if you had a 3x3x3 grid

like the one I drew

[clear hill]

k

[tribal roost]

so MEO doesn't work with mine for example

although it's way more fun if it does

[clear hill]

ok

wait

[tribal roost]

I mean for the purpose of this exercice

[clear hill]

i found a video on this exact question

[tribal roost]

oh cool

[clear hill]

im watching it right now

[tribal roost]

well I think you can def understand it without me

[clear hill]

uhh

[tribal roost]

And I gtg sleep

[clear hill]

o

ok

[tribal roost]

so bye

[clear hill]

bye

OHHHHHHHHHHHHHH

I UNDERSTAND IT NOW

ITS THREE SHEETS STACKED ON TOP OF EACHOTHER

NOT A CUBE

😲

[marsh citrus]

@clear hill Has your question been resolved?

[marsh citrus]

@clear hill Has your question been resolved?

[marsh citrus]

@clear hill Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cyan gazelle]

Can you help me solve these problems?

[cyan gazelle]

I was absent during the discussion and I just don’t understand it 😭

[marsh citrus]

@cyan gazelle Has your question been resolved?

[odd orchid]

whats the general formula of an ellipse

[marsh citrus]

@cyan gazelle Has your question been resolved?

[cyan gazelle]

I think it’s ((x-h)²/a²) + ((y-k)²/b²) = 1

[brisk blade]

It's correct

[brisk blade]

U need to know the coordinates of foci

do you have any idea abt them?

[bitter badger]

You need to first identify the orientation (horizontal or vertical) by comparing the coordinates of the center with those of the focus or vertex. If the x-coordinates match, the major axis is vertical, and if the y-coordinates match, it's horizontal. This determines which standard form to use:
(x-h)^2/b^2+ (y-k)^2/a^2= 1 (Vertical)
or
(x-h)^2/a^2+ (y-k)^2/b^2= 1 (Horizontal)
Then, use the given information to find the key values: the distance from the center to a vertex is a (the semi-major axis), the distance from the center to a focus is c, and the length of the major axis is 2a. Once you have a and c, use the fundamental relationship for an ellipse, c^2 = a^2 - b^2, to calculate b^2 (the square of the semi-minor axis). Then lstly, substitute the center (h, k), a^2, and b^2 into the correct standard equation. For the drawing part, plot the center, and use a and b to find the four vertices, and use c to find the two foci, then sketch the smooth curve

(If you need more help and my yap doesnt make sense lmk😭)

[cyan gazelle]

Isn’t that the 2 points which is the focus?

[cyan gazelle]

Oml, I actually understand it better now

[brisk blade]

Yep

[cyan gazelle]

I’ll try to solve it again now, can you chk if I’m correct?

[brisk blade]

Sure

js make sure you know the concepts first

[cyan gazelle]

It’ll prob take some time tho 🤦🏻‍♀️

[brisk blade]

Fine

[cyan gazelle]

Yes yess

[brisk blade]

Or else I'll solve one for you

[cyan gazelle]

That could work as well BAHAHHAHAHAH but I have to learn it

[brisk blade]

Fine , as you wish

Do you have the answer key?

[cyan gazelle]

Noo, it's an assignment

Why?

[cyan gazelle]

I’ll close/free this channel so that others can use it for the mean time 😅

.close

[marsh citrus]

Channel closed

Closed by @cyan gazelle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jagged swift]

Can someone help me.

[jagged swift]

I have provide the working out above.

I am not sure what to do next.

(3x+ax) ?

[turbid mica]

then you have $2x^2 + ax + 2$ left over and that $x^2 + 1$ is a factor of it

[elfin berry]

fright

[turbid mica]

wait what

oh ok

hold on

ok

[turbid mica]

yeah pretty much but i would write it as (a + 3)x
you would then have $2x^2 + (a + 3)x + 2$ left over and $x^2 + 1$ needs to cleanly divide into that
so then you would write + 2 for the quotient and get $(a + 3)x$ left over
to have $x^2 + 1$ be a factor of the original quartic, there must be no remainder
which means $a + 3 = 0 \Rightarrow a = -3$

[elfin berry]

fright

[jagged swift]

k

oh ok

thankyou

.close

[marsh citrus]

Channel closed

Closed by @jagged swift

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unkempt berry]

Why is this wrong

[vagrant raft]

the negation of "implies" is not "implies"

[unkempt berry]

i dont understand

[vagrant raft]

the negation of "teaches(x, y) ^ grades(x, y) -> reviews(x, y)" is not what you wrote

[unkempt berry]

yes its wrong

[vagrant raft]

the negation of $A \rightarrow B$ is: $\text{not} (B) \wedge A$

[elfin berry]

bloubbloub

[unkempt berry]

how do you know that?

[vagrant raft]

I thought you would have covered it in class

the only time when A doesn not imply B is when A is true but B is not

[unkempt berry]

true we only got the materials but not really explained the reasons behind the reasonings

[leaden monolith]

Look at a truth table

[unkempt berry]

im guessing thats inferring from the truth table

[leaden monolith]

That’s nearly always the answer with these things

[unkempt berry]

yea

[leaden monolith]

I swear ive said this to every logic problem I’ve seen posted here in the last 2 days

[unkempt berry]

my first time asking for the predicates

any other tips?

[wary lichen]

Its mostly because
$p \implies q$ is logically equivalent to: $\neg p \vee q$

[elfin berry]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[unkempt berry]

this is conflicting

[vagrant raft]

no it's the same

[unkempt berry]

ow

[vagrant raft]

I did the negation

[wary lichen]

What you was told there is the negation of "implies"

If you learnt De Morgan's Law, you can see why the negation of implies is $p \wedge \neg q$

[elfin berry]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[unkempt berry]

we only got this for De Morgan's

[wary lichen]

Its technically a pair of laws. Although both are essentially the same idea

The negation of AND or OR is the opposite, with negated truth values.

[wary lichen]

Try to apply it here, negate the last part of this

[unkempt berry]

alright i understand

[wary lichen]

It so happens to be that "not implies" doesnt see much use as a symbol cause linguistically speaking, it doesnt make much sense compared to the formal logic.

So we just write the wedge

[unkempt berry]

hmmm

understood

.close

[marsh citrus]

Channel closed

Closed by @unkempt berry

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tidal crane]

part (b) i understand why its 6.5, but i dont understand 10.5

[fervent rampart]

the graph switches from concave down to concave up somewhere around there

[tidal crane]

so is acceleration always 0 when at that point

.close

[marsh citrus]

Channel closed

Closed by @tidal crane

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[karmic oasis]

Hi, the question asks to find the exact value of x. I am new too this area of trig and just have been experiencing difficulty in understanding why the answer is sqroot30/2. If someone could explain it that would be great.

[viral cedar]

so, do you know about similarity?

[karmic oasis]

yeah somewhat

Ive dont it in the past

[viral cedar]

do you agree that any triangle with this type of angle configuration is similar

and therefore has same side ratios

[karmic oasis]

yeah

[viral cedar]

ok so basically we take a right angle triangle and vary an acute angle

[karmic oasis]

I just wanna preface, I js started this unit

[viral cedar]

what

is

a

preface

[karmic oasis]

wait nvm sorry i meant like

im js new to this aspect of trig

so like some terminology is new yk

[viral cedar]

which ones

[karmic oasis]

vary an acute angle

vary spec

[viral cedar]

vary means "change"

[karmic oasis]

okay

[viral cedar]

and while we change this one angle, we keep track of all the side ratios. this is useful because any triangle that has the same angles has the same ratios as well

[karmic oasis]

ahh right

[viral cedar]

so, the ratios depend only on the angle alpha. we can take the value of alpha and get the ratios. we define:
sin($\alpha$) = $\frac{b}{c}$
cos($\alpha$) = $\frac{a}{c}$
sin($\alpha$) = $\frac{b}{a}$

[elfin berry]

mango_bird

[karmic oasis]

yep

[viral cedar]

and, how might we use this to solvbe the question?

[karmic oasis]

use the one that includes the given point and the missing one

so

cos

[viral cedar]

exactly

and cos(30) is

[karmic oasis]

sqroot 3/2

[viral cedar]

which is x over sqrt10

[karmic oasis]

ye

[viral cedar]

what is x

[karmic oasis]

OMG u just solve for x

[viral cedar]

yeah lol

[karmic oasis]

ohhh thats why its sqroot 30/2 😭

i was trying to equate sq root 10 and 2

[viral cedar]

turns out you alr know trig i shouldnt have yapped that long

😭

[karmic oasis]

LMAOOO its okay

but one question

how do you remember everything

like what everything equals

[viral cedar]

so this is where the famous "sohcahtoa" comes in

[karmic oasis]

i meant more spec

like

[viral cedar]

oh ik

[karmic oasis]

the different equations of certain angles

30 degrees, 40 etc etc

[viral cedar]

you only have to memorise 30 degrees

im not sure sin(40) is even algebraic so....

[karmic oasis]

SORRY i meant 45

[glossy flint]

Well, that's half a square so it's easy to derive

[viral cedar]

well, do you find it hard to memorise that "the two short ones are equal"

[glossy flint]

Since diagonal = √2 • side

[karmic oasis]

idk i js want to be able to quickly identify it in a test

like no brainer,

[viral cedar]

its an isoceles triangle so

ofc they are equal

180-90-45=45

[karmic oasis]

wait yeah

okay thanks for ur help I think I'm pretty set for now \

.close

[marsh citrus]

Channel closed

Closed by @karmic oasis

Use .reopen if this was a mistake.

[glossy flint]

https://youtube.com/shorts/lq-GkMcDpUU?si=nJJBd2sj0Wd8eEzS

This might help

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sturdy jackal]

Lim r->0 ((e^(2k+h)-h-2k-1)e^6)/root(h^2+k^2)

[sturdy jackal]

Need it to be 0

[paper raptor]

[\lim_{(h,k)\to(0,0)}\frac{(e^{2k+h}-h-2k-1)e^6}{\sqrt{h^2+k^2}}]

well there's no r in the limit expression

[sturdy jackal]

Mb (h,k)->(0,0)

[elfin berry]

ΠαϳαμαΜαμαΛλαμα

[paper raptor]

well if you approach along h=0 or k=0 do you get different results?

[sturdy jackal]

Haven’t tried but usually we’re meant to convert to polar coordinates

I also saw something about maclaurin series

[marsh citrus]

@sturdy jackal Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wet panther]

222. Calculate that

[fervent tapir]

hm?

did you accidentally hit enter too early?

[wet panther]

It's not sending

My WiFi slow sorry

[fervent tapir]

nps

[odd orchid]

first calculate the geometric sequence

[wet panther]

,rccw

[wet panther]

This is what I wrote before giving up

[fervent tapir]

,rccw

[odd orchid]

do you know how to evaluate a geometric sequence

[wet panther]

So I did it wrong?

[odd orchid]

uh i cant really read what youre doing bur im guessing that youre trying to add the fractions individually

[wet panther]

Idk I got that q is 3 2/27 which idk if that's right

[odd orchid]

find out what $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} \cdots$ is

[elfin berry]

ashy!

[wet panther]

Okay and how? Sn=b1/1-q ?

[odd orchid]

formula for geomtric sequence is a/(1-r)

[wet panther]

Oh that

Isn't that basically what I wrote or?

Bc idk r

Nor q bc idk if it's right

[odd orchid]

r is the common ratio

what is the factor between one term and the next

[wet panther]

Oh so q okay so I think I didn't find it

I got $3 \frac{2}{27}$

[elfin berry]

supanova (Oh Ay)

[wet panther]

Idk how to write it here

[next ivy]

hi, please open your own channel

[odd orchid]

follow the formula

what is a and r

[jovial robin]

how to open channel

[wet panther]

a is 3^1 and r is 3^2/27

Idk

Well my WiFi is bad

Thx tho

.close

[marsh citrus]

Channel closed

Closed by @wet panther

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lament spruce]

Plz help me how to solve this problem

🙁

oh no nothing

sr

mb

.close

[marsh citrus]

Channel closed

Closed by @lament spruce

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ornate shale]

Hiiii, I'm stuck midway on this problem

[ornate shale]

I reduced this to

$\pi\int_{0}^{\frac{\pi}{2}}\frac{\sin\left(x\right)}{1+\sin^{2}\left(x\right)}dx$

But I'm not sure what to do next, I can't find the closed form of this integral

[elfin berry]

Poly(^///^)

[odd orchid]

can you not solve using kings rule from the start?

may be wrong cos im doing it in my head but i feel like that may lead to somewhere

[ornate shale]

I haven't thought of that, I'll try

[quick kindle]

you reduce to this form using kings rule

here u can probably sub u=cosx

cuz denom then becomes 2-u^2

[static quarry]

do you mean u = cos x?

[quick kindle]

yes

[ornate shale]

I tried that sub but I can progress any longer after

[ornate shale]

Oh

[boreal rock]

Again substitute 2-u²=t

[odd orchid]

integral will be 1/(2-u^2), that substitution wont help

[ornate shale]

$\frac{-\sqrt{2}\pi}{4}\left(-\ln\left(1-\frac{\cos\left(\pi\right)}{\sqrt{2}}\right)+\ln\left(1+\frac{\cos\left(\pi\right)}{\sqrt{2}}\right)\right)$

[elfin berry]

Poly(^///^)

[ornate shale]

I got this

Man I feel dumb

[ornate shale]

I took 2 outside and sub u/sqrt(2)=t

Thanks guys

Btw how can I spot the cos(x) sub

Maybe I'm not doing enough problems to figure that out

[odd orchid]

from the sin x dx

[boreal rock]

U can just use partial fractions

[ornate shale]

okay makes sense

[ornate shale]

Oh yeah haha, but I'm more familiar with 1-x^2

Thanks everyone

.close

uh

.close ?

why doesn't the bot come out

.reopen

.close

uhh....

[sweet sparrow]

.close

bot is down

.close

[marsh citrus]

Channel closed

Closed by @sweet sparrow

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[white current]

Being asked to prove G ≈ G, G ≈ H implies H ≈ G, and G ≈ H & H ≈ K implies G ≈ K

[white current]

This is what I've got so far, but I kind of stalled out

[glass silo]

Bear in mind that you've done the "bijective" bit (though I would ask "but why?" for both ), but anyways, you want to also show that the inverse is a homomorphism too

Also you don't want to define your original isomorphism "explicitly", as you don't necessarily know what it would be, just that [at least] one exists

So you can say that you have an isomorphism from G to H, then show that the inverse map must also be an isomorphism too

[white current]

so you're suggesting I start from H^-1 and work back to G?

or... I'm not sure I'm wording that right

[glass silo]

What I'm suggesting is more that, you have that $G$ is isomorphic to $H$, so you know that you have some bijective $\sigma : G \to H$ such that $\sigma(g_1 g_2) = \sigma(g_1) \sigma(g_2)$ for any pair of $g_1, g_2 \in G$

[elfin berry]

@glass silo

[white current]

All right, following so far

[glass silo]

Now, you take $\sigma^{-1} : H \to G$ (you know that exists by the bijective bit etc etc), and now, what we wanna verify is whether $\sigma^{-1}(h_1 h_2) = \sigma^{-1}(h_1) \sigma^{-1}(h_2)$ for any pair $h_1, h_2 \in H$

[elfin berry]

@glass silo

[glass silo]

So, does that hold?

[white current]

Going with yes

but on more of a "I feel like it does" level than a "yes and I know why" level

[glass silo]

Grrrr, I thought you'd say that well then, do you wanna try and work through it together then?

[white current]

in theory yes but one of my other classes is about to start :(

[glass silo]

Awwww, that's fair enough if anything, you can always come back after you're done and you have a bit more time, and I'm sure someone will be happy to help (and if I'm still about, I would be more than glad to, of course )

[white current]

prof lets us do corrections on homework as long as we make a solid attempt at the problem first, and you've at least given me a new angle to consider, so might try to spend some time attempting to work it out myself some more first

appreciate it tho 🫡

.close

[marsh citrus]

Channel closed

Closed by @white current

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.